Why a Call Butterfly Can Have Negative Initial Value

Summary

The document examines a three-strike call position: buying calls at the lower and higher strikes while selling two calls at the middle strike, all with the same expiration. It asks why the position can have a negative value at inception. The replies point to the distinction between an option strategy’s payoff at expiration and the current market value of its component options.

The discussion suggests inspecting each option’s price and the combined payoff across possible terminal underlying prices. It notes that the payoff is nonzero over part of the price range, so the portfolio should not be presumed to have zero initial value. The explanations are brief and do not provide a pricing model, numerical option values, or a full payoff derivation; one reply also appears to confuse calls and puts. The example is best treated as a prompt to analyze the legs and states carefully rather than as a complete valuation argument.

Key ideas

• A multi-leg option payoff does not determine that its initial market value is zero.
• The position combines calls at three strikes, with two short calls at the middle strike.
• Analyzing component option prices helps explain the net initial debit or credit.
• Checking the payoff across terminal prices can reveal where the position has nonzero payoff.

Tags

# Why the value of this portfolio is negative?


# Why the value of this portfolio is negative?












Let's assume

- I buy 1 call with strike 100 and 1 call with strike 120

- I sell 2 calls with strike 110

(with same expiration)

I wonder why value of this portfolio is negative at $t=0$?

## Answer by arodrisa (score 1)

https://quant.stackexchange.com/a/20829

You need to check them individually and understand how option pricing works. Then you will realize that you want to sell 2 put options Deeply in the money(cheap to buy), buy one call option At the money (a bit expensive) and finally buy an "Out of the money" call option (cheap). So you are trying to finance something a bit expensive by selling something cheap, therefore you need to add some of your cash. That is why it is negative.

Try to draw, and use numeric examples to understand it.

## Answer by user32416 (score -1)

https://quant.stackexchange.com/a/20822

This portfolio clearly doesn't have value of $0$ at $t = 0$. Ignoring the fact that you seem to have confused payoffs of option strategies and the value of a portfolio of options, even the payoffs themselves as given here will have state where the payoff is nonzero (i.e. $S_T \in [100,110]$). This by itself ensures that no matter what model you use for asset prices, you'll enjoy a nonnegative value to this portfolio at $t = 0$.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.